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#Trapzoidal Reel by @mathvisualproofs - Zeno in an Equilateral Triangle This is a short, animated visual proof demonstrating the sum of an infinite geometric series using a dissection proof
34.5K
MA
@mathvisualproofs
Zeno in an Equilateral Triangle This is a short, animated visual proof demonstrating the sum of an infinite geometric series using a dissection proof in an equilateral triangle. In particular, we show how to find the sum of powers of 1/2 in the equilateral triangle. Geometric series are important for many results in calculus, discrete mathematics, and combinatorics. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! Also, check out my playlist on geometric sums/series: https://youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw This animation is based on a proof by Stephan Berendonk (2020) from the November 2020 issue of The College Mathematics Journal, (https://doi.org/10.1080/07468342.2020.1830649 p. 385) ​ ​ #math​ #calculus​ #manim​​ #proofwithoutwords​ #geometricseries equilateraltriangle To learn more about animating with manim, check out: https://manim.community
#Trapzoidal Reel by @socraticmathematics - Trigonometry is all about the unit circle. Other trigonometric functions is coming… #mathart #mathanimation #manim #unitcircle
1.5K
SO
@socraticmathematics
Trigonometry is all about the unit circle. Other trigonometric functions is coming… #mathart #mathanimation #manim #unitcircle
#Trapzoidal Reel by @promath_science - V𝒊𝒔𝒖𝒂𝒍 𝑴𝒂𝒕𝒉 𝑪𝒐𝒏𝒄𝒆𝒑𝒕: 𝒕𝒉𝒆 𝒔𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒊𝒏𝒇𝒊𝒏𝒊𝒕𝒆 𝒈𝒆𝒐𝒎𝒆𝒕𝒓𝒊𝒄 𝒔𝒆𝒓𝒊𝒆𝒔 𝒘𝒊𝒕𝒉 𝒇𝒊𝒓𝒔𝒕 𝒕𝒆𝒓𝒎 1/8 𝒂𝒏�
1.5K
PR
@promath_science
V𝒊𝒔𝒖𝒂𝒍 𝑴𝒂𝒕𝒉 𝑪𝒐𝒏𝒄𝒆𝒑𝒕: 𝒕𝒉𝒆 𝒔𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒊𝒏𝒇𝒊𝒏𝒊𝒕𝒆 𝒈𝒆𝒐𝒎𝒆𝒕𝒓𝒊𝒄 𝒔𝒆𝒓𝒊𝒆𝒔 𝒘𝒊𝒕𝒉 𝒇𝒊𝒓𝒔𝒕 𝒕𝒆𝒓𝒎 1/8 𝒂𝒏𝒅 𝒓𝒂𝒕𝒊𝒐 1/2. 𝑻𝒉𝒊𝒔 𝒂𝒏𝒊𝒎𝒂𝒕𝒊𝒐𝒏 𝒊𝒔 𝒃𝒂𝒔𝒆𝒅 𝒐𝒏 𝒂 𝒗𝒊𝒔𝒖𝒂𝒍 𝒑𝒓𝒐𝒐𝒇 𝒇𝒓𝒐𝒎 𝒕𝒉𝒆 𝒘𝒐𝒏𝒅𝒆𝒓𝒇𝒖𝒍 𝒃𝒐𝒐𝒌 𝑪𝒉𝒂𝒓𝒎𝒊𝒏𝒈 𝑷𝒓𝒐𝒐𝒇𝒔 𝒃𝒚 𝑪𝒍𝒂𝒖𝒅𝒊 𝑨𝒍𝒔𝒊𝒏𝒂 𝒂𝒏𝒅 𝑹𝒐𝒈𝒆𝒓 𝑵𝒆𝒍𝒔𝒆𝒏 #mathvisualthinking #geometricseries #mc2indore
#Trapzoidal Reel by @mathvisualproofs - Pi From Three Arctangents This is a short, we show a wonderful way to see that pi is the sum of three arctangents: the arctangent of 1, 2 and 3. If
149.6K
MA
@mathvisualproofs
Pi From Three Arctangents This is a short, we show a wonderful way to see that pi is the sum of three arctangents: the arctangent of 1, 2 and 3. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! Also, check out my playlist on Pi: https://youtube.com/playlist?list=PLZh9gzIvXQUsGRDvzvXc02lDIKHaVeFwq&si=9YdPTM5O_WT2o1KN This animation is based on a proof by Edward M. Harris from the March 1987 issue of The College Mathematics Journal : https://www.jstor.org/stable/2686505 , page 141 ​#math​ #pi​ #manim​ #trigonometry #proofwithoutwords To learn more about animating with manim, check out: https://manim.community
#Trapzoidal Reel by @insightcreativesociety - We often treat math as a collection of abstract rules. In reality, it is grounded in physical space. Here is one way to show why the formula is actua
220
IN
@insightcreativesociety
We often treat math as a collection of abstract rules. In reality, it is grounded in physical space. Here is one way to show why the formula is actually correct. When you can see the logic, you no longer need to rely on memorization. #insightcreativesociety #pythagoreantheorem #geometry
#Trapzoidal Reel by @hannekekkonen - Why is the limit of the lengths of curves not necessarily the length of the limit curve? If the diameter has length 2 the corresponding semicircle ha
7.0K
HA
@hannekekkonen
Why is the limit of the lengths of curves not necessarily the length of the limit curve? If the diameter has length 2 the corresponding semicircle has length π. The same is true for each curve obtained by replacing every semicircle by two half sized semicircles: every one of these curves still has total length π. As the process continues, the curves get closer and closer to the diameter. But their lengths do not get closer to 2. The arrows show the direction of travel along the curves. Although the curves themselves converge to the diameter, their directions (or derivatives) do not converge to the direction along the diameter. Instead of settling down to the constant direction of a straight line, they keep oscillating up and down faster and faster. At the risk of repeating a cliché: it’s not the destination, it’s the journey. The length of a curve is given by the integral of its speed. So even though the curves get arbitrarily close to the straight line, they are still travelled in a very different way, and their lengths stay equal to π rather than approaching 2. #pi #math #mathematics #matheducation #geometry #arclength #derivative #visualproof #mathfacts #mathart #mathfun #onderwijs #wiskunde #meetkunde
#Trapzoidal Reel by @chabemaths - 1500 circles draw a famous face. A math art animation made with Fourier series, epicycles, and rotating circles. Can you guess who it is? #math #mat
2.5K
CH
@chabemaths
1500 circles draw a famous face. A math art animation made with Fourier series, epicycles, and rotating circles. Can you guess who it is? #math #mathart #fourier #epicycles #geometry
#Trapzoidal Reel by @erik_alan_norman - Dynamic retopo but make it ✨procedural✨. #topology #geometry #math #creativecoding #simulation
5.1K
ER
@erik_alan_norman
Dynamic retopo but make it ✨procedural✨. #topology #geometry #math #creativecoding #simulation
#Trapzoidal Reel by @patterns.click - We derived the equation of the three-body problem. Core formula: iℏ∂tψ/∂t=−(ℏ2/2m)∇2ψ+V(x)ψiℏ∂ tψ/∂t=−(ℏ 2/2m)∇ 2ψ+V(x)ψ.3bodies Then we animated it.
144
PA
@patterns.click
We derived the equation of the three-body problem. Core formula: iℏ∂tψ/∂t=−(ℏ2/2m)∇2ψ+V(x)ψiℏ∂ tψ/∂t=−(ℏ 2/2m)∇ 2ψ+V(x)ψ.3bodies Then we animated it. 🌀 Parametric fractal + Japanese Sayagata geometric overlay ⚫ Schrödinger prob as structural core No closed solution exists — but patterns do. This is investigation through animation. Equation over equation. Chaos over geometry. #ThreeBodyProblem #SchrodingerEquation #ParametricFractal #SayagataPattern #GeometricOverlay #UnsolvedPhysics #MathArt #GenerativeAnimation
#Trapzoidal Reel by @eulerism_ - Uzumaki A spiral that repeats, folds, and evolves without end. In a broader sense, it reflects the idea of fractal geometry, where simple rules genera
2.4K
EU
@eulerism_
Uzumaki A spiral that repeats, folds, and evolves without end. In a broader sense, it reflects the idea of fractal geometry, where simple rules generate patterns that echo themselves across scales. What looks like a single curve becomes a structure that carries its form infinitely inward and outward. This visualization traces that idea. A curve shaped by mathematics, unfolding into layers of repetition and variation, where each turn mirrors the last, yet never remains exactly the same. Fractals are not just shapes. They are processes. Growth, iteration, and recursion captured in motion. What begins as a line becomes a world of patterns. Mathematics does not draw spirals. It creates systems where spirals emerge. #uzumaki #fractal #fractalanimation #mathematics #mathvisualization #mathart #geometry #recursion #sciencevisualization #stem #mathedit
#Trapzoidal Reel by @aman.kumar.3348 - Animation through using graphs! #math #playing #graphics #geometry #graphs
3.8K
AM
@aman.kumar.3348
Animation through using graphs! #math #playing #graphics #geometry #graphs

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